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"Full-wave" electromagnetic analysis means that the solution is obtained by solving Maxwell's equations for the electric and magnetic fields in the time domain or the frequency domain. This type of rigorous analysis, when performed for the general 3D case, makes no simplifying assumptions about the nature of the EM problem. When using a full-wave 3D EM solver, the usual constraints are solve time and/or problem size.
Other EM analysis methods, such as those based on ray-tracing, usually make an assumption about the problem, such as the object being modeled is large compared to a wavelength. These are used when possible (when all of the assumptions are valid) to avoid the long run-times and size limitations that can accompany general full-wave methods.
Hybrid codes combine a full-wave method with another method (sometimes called high-frequency or asymptotic) to increase the range of problems that can be solved with the tool.
"Full wave" is a term that I first heard in the early 1980's. I think it was introduced by Prof. Rolf Jansen, whom I hold in very high respect. However, while the term sounds impressive, I think it is inappropriate simply because it's opposite, "partial wave" makes no sense. I usually say "full electromagnetic analysis" to indicate that the only approximation to Maxwell's equations is in the meshing of the problem. There is no approximation in terms of using approximations for the Green's functions, etc. "Full electromagnetic analysis" is both more specific and also requires one less word as compared to "full wave electomagnetic analysis".
The term "full-wave" is often compared to the term "quasi-static". In this context, it means that the full electromagnetic wave-based solution is performed instead of assuming that the circuits or components are small compared to a wavelength.
For example, the Momentum tool offered by Agilent includes both a quasi-static solver and a full-wave EM solver. The user can choose which mode to use depending on the problem. Agilent recommends using the "full-wave" solution for structures over one-half wavelength in size. The advantage of quasi-static methods is that the solve time is much faster.
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